First-principles study on the high-pressure physical properties of orthocarbonate Ca2CO4

Orthorhombic Ca2CO4 is a recently discovered orthocarbonate whose high-pressure physical properties are critical for understanding the deep carbon cycle. Here, we study the structure, elastic and seismic properties of Ca2CO4-Pnma at 20–140 GPa using first-principles calculations, and compare them with the results of CaCO3 polymorphs. The results show that the structural parameters of Ca2CO4-Pnma are in good agreement with the experimental results. It could be the potential host of carbon in the Earth's mantle subduction slab, and its low wave velocity and small anisotropy may be the reason why it cannot be detected in seismic observation. The thermodynamic properties of Ca2CO4-Pnma at high temperature and high pressure are obtained using the quasi-harmonic approximation method. This study is helpful in understanding the behavior of Ca-carbonate in the Earth’s lower mantle conditions.


Methods
First-principles calculations are done with using the VASP package 46,47 with projector-augmented wave 48 . The exchange-correlation interactions adopt the Perdew-Burke-Ernzerhof functional within the generalized gradient approximation 49 . The electronic configurations of the atoms are Ca: 3s 2 3p 6 4s 2 , C: 2s 2 2p 2 , O: 2s 2 2p 4 , respectively. The cutoff energy of the plane-wave basis is set to 900 eV. The k-point mesh generation and data processing are obtained by vaspkit program 50 . The k-points mesh of Ca 2 CO 4 -Pnma, calcite, aragonite, P2 1 /c-l, post-aragonite, P2 1 /c-h and C222 1 are set to 5 × 7 × 4, 9 × 9 × 2, 7 × 4 × 6, 7 × 10 × 3, 8 × 7 × 8, 8 × 10 × 4, and 6 × 5 × 10 using the Monkhorst-Pack scheme 51 , respectively. The convergence criteria for energy and force are 1.0⨯10 -8 eV and 0.02 eV/Å, respectively. Based on the optimized lattice structure, the stress-strain method is used to obtain the elastic stiffness tensor. In order to ensure the accuracy of the elastic constants of Ca 2 CO 4 -Pnma, the elastic constants of calcite and aragonite are calculated and compared with the available experimental results 32,33 . As shown in Table S1 (see Supplementary Material), the calculated results are in good agreement with the experimental results 32,33 . The thermodynamic properties are calculated using the quasi-harmonic approximation method 52 of the PHONOPY program 53,54 , and the force constants are calculated using the density functional perturbation theory 55 . The supercells of aragonite and Ca 2 CO 4 -Pnma adopt 2 × 2 × 2 and 2 × 2 × 1 unit cells, respectively. The convergence tests of the phonon spectrum calculations of aragonite and Ca 2 CO 4 -Pnma are shown in Tables S2,  S3, and Figs. S1-S8 (see Supplementary Material).

Results and discussion
Structural properties. The lattice parameters and equations of state for Ca 2 CO 4 -Pnma are presented in Fig. 1. It is found that the calculated results are in good agreement with the available experimental 24 and previous theoretical results 21,24 , indicating the validity of the structure. The sensitivity of the axis to compression is c > b > a. The unit-cell volume at 0 GPa is 303.38 Å 3 and the bulk modulus and its first pressure derivative are K 0 = 113.40 GPa and K 0 ′ = 4.00 by fitting the third-order Birch-Murnaghan equation, respectively, which are consistent with the results (V 0 = 302.0(3) Å 3 , K 0 = 108(1) GPa, and K 0 ′ = 4.43 (3)) of Binck et al. 24 . In order to better understand the elastic and seismic properties of Ca 2 CO 4 -Pnma, the candidate CaCO 3 structures (aragonite, P2 1 /c-l, post-aragonite, P2 1 /c-h, C222 1 , '− l = low pressure' , '− h = high pressure') in the Earth's mantle are considered. The relative stabilities of the CaCO 3 polymorphs considered in this work are evaluated from their enthalpies. According to Fig. S9 (see Supplementary Material), P2 1 /c-l stabilizes above 30 GPa and retains its stability up to 46 GPa, while P2 1 /c-h stabilizes above 75 GPa and retains its stability up to at least 140 GPa, which are consistent with the experimental and previous theoretical results 3,5 . CaCO 3 -C222 1 above 137 GPa is stable relative to post-aragonite, but this does not make any sense 5,56 . Because in this interval, the modification P2 1 /c-h is more favorable. For comparison with calcium orthocarbonate, four modifications of    Fig. 2 and Table 1.
Within the studied pressure range, c 11 > c 22 > c 33 , indicating that compression is easier along the c-axis than along the a-and b-axes. These results are consistent with those of Fig. 1, where the lattice parameter c decreases faster than the lattice parameters a and b with increasing pressure. The calculated elastic constants of CaCO 3 polymorphs are shown in Figs. S10-S13 and Tables S4-S7 (see Supplementary Material), respectively. Therefore, we believe that the calculated elastic constants are correct, but experimental verification is required. The bulk modulus (B) and shear modulus (G) of Ca 2 CO 4 -Pnma can be obtained by the Voigt 57 -Reuss 58 -Hill 59 scheme. As can be seen from Fig. 3 and Table 1, B is greater than G, indicating that with the change of volume, Ca 2 CO 4 -Pnma is more and more difficult to be compressed, and G is the main factor for the deformation of  In order to evaluate the elastic anisotropy of Ca 2 CO 4 -Pnma, we adopt the scheme of Ravindran et al. 60 . The shear anisotropic factors of A 100 in (100) plane, A 010 in (010) plane, and A 001 in (001) plane can be obtained from the following expression: The variation of shear anisotropic factors A 100 , A 010 and A 001 of Ca 2 CO 4 -Pnma with pressure is displayed in Fig. 4 and Table 1. A 010 and A 001 gradually decrease with increasing pressure, A 100 first increases with the increase of pressure, and then gradually decreases at > 40 GPa. It can also be found that the elastic anisotropy of Ca 2 CO 4 -Pnma in the lower mantle conditions is very small, and the anisotropy of the (010) plane between [101] and [001] directions is the smallest.
The compressional and shear wave velocities of minerals can be calculated from the elastic constants and densities. The compressional (V P ) and shear (V S ) wave velocities of Ca 2 CO 4 -Pnma and CaCO 3 polymorphs can be obtained from the Navier's equations 61 : (1) A 100 = 4c 44 c 11 + c 33 − 2c 13    62 are displayed in Fig. 5 and Table 1. From Fig. 5a, it is found that the densities of Ca 2 CO 4 -Pnma in the lower mantle is less than those of PREM, and greater than those of CaCO 3 polymorphs. As shown in Fig. 5b, the V P and V S of CaCO 4 -Pnma and CaCO 3 polymorphs are lower than those of PREM, and the V P and V S of Ca 2 CO 4 -Pnma are greater than those of P2 1 /c-l and post-aragonite, which are almost the same as those of P2 1 /c-h. The wave velocities in various crystallographic directions can be obtained by solving the Christoffel equation C ijkl n j n l − ρV 2 δ ik = 0 63 . Figure 6  The anisotropy A P of the compressional waves and the polarization anisotropy A S of the shear waves are defined as 65 : Figure 7 and Table 1 show the A P and A S of Ca 2 CO 4 -Pnma and CaCO 3 polymorphs. It can be seen that the seismic anisotropy A P and A S of Ca 2 CO 4 -Pnma are less than those of CaCO 3 polymorphs, and decrease with the increase of pressure, and gradually increase at > 45 GPa. The nonlinear dependence of seismic anisotropy on pressure can be attributed to the nonlinear pressure sensitivity of the wave velocity, which is caused by the nonlinear pressure dependence of its elastic modulus, especially the shear modulus.
The seismic properties of Ca 2 CO 4 -Pnma indicate that it could be the potential host of carbon in the subduction slab and coexists with CaCO 3 polymorphs, as suggested by Sagatova et al. 21,23 . It was also verified by Binck et al. 24 . The low wave velocity and small anisotropy of Ca 2 CO 4 -Pnma may be one of the reasons why it is impossible to detect the presence of carbonate in the lower mantle during the seismic observation of the subduction slab. Thermodynamic properties. The thermodynamic parameters of minerals are a prerequisite for deriving the thermal state of the Earth's interior. In order to obtain the variation of thermodynamic parameters of Ca 2 CO 4 -Pnma with temperature and pressure, we first verify the constant pressure heat capacity C P of aragonite at 0 GPa, and find that the calculated results are in good agreement with the experimental results 44 (Fig. 8). On this basis, the predicted heat capacity and thermal expansion coefficient α of Ca 2 CO 4 -Pnma are shown in Figs. 9 and 10, respectively. www.nature.com/scientificreports/ Figure 9 shows that the constant capacity heat capacity C V increases sharply with increasing temperature at low temperatures. Due to the suppression of non-harmonic effects under high pressure, the constant volume heat capacity C V under high pressure and high temperature is very close to the Dulong Petit limit. The constant pressure heat capacity C P is very close to the constant capacity heat capacity C V . In addition, the effects of temperature and pressure on constant capacity heat capacity C V and constant pressure heat capacity C P are opposite, and the impact of temperature is more noteworthy.
It can be seen from Fig. 10 that thermal expansion coefficient α at low temperature increases rapidly with the increase of temperature and tends to flatten rapidly with the increase of temperature. With the increase of pressure, the thermal expansion coefficient α decreases rapidly, and the influence of temperature becomes less and less obvious, resulting in linear high temperature behavior.

Conclusions
On the basis of the determination of the stability for CaCO 3 polymorphs in the lower mantle conditions and the verification of the structural parameters of Ca 2 CO 4 -Pnma, we study the elastic, seismic and thermodynamic properties of Ca 2 CO 4 -Pnma, and compared the results with those of CaCO 3 polymorphs. The research shows that the densities of Ca 2 CO 4 -Pnma in the lower mantle are greater than those of CaCO 3 polymorphs, and the seismic anisotropies are less than those of CaCO 3 polymorphs. The wave velocities of Ca 2 CO 4 -Pnma and CaCO 3 polymorphs are relatively low, and the wave velocities of Ca 2 CO 4 -Pnma and CaCO 3 -P2 1 /c-h are almost the same.

Data availability
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.